We present a hybrid code combining the OpenMP-parallel tree code VINE with an algorithmic chain regularization scheme. The new code, called "rVINE", aims to significantly improve the accuracy of close encounters of massive bodies with supermassive black holes in galaxy-scale numerical simulations. We demonstrate the capabilities of the code by studying two test problems, the sinking of a single massive black hole to the centre of a gas-free galaxy due to dynamical friction and the hardening of a supermassive black hole binary due to close stellar encounters. We show that results obtained with rVINE compare well with NBODY7 for problems with particle numbers that can be simulated with NBODY7. In particular, in both NBODY7 and rVINE we find a clear N-dependence of the binary hardening rate, a low binary eccentricity and moderate eccentricity evolution, as well as the conversion of the galaxy's inner density profile from a cusp to a a core via the ejection of stars at high velocity. The much larger number of particles that can be handled by rVINE will open up exciting opportunities to model stellar dynamics close to SMBHs much more accurately in a realistic galactic context. This will help to remedy the inherent limitations of commonly used tree solvers to follow the correct dynamical evolution of black holes in galaxy scale simulations.